數線上的分點公式(1)
Author: 藍邦偉  老師

$ O $

$ 數線上的分點公式$
$(1)\;內分點公式$

$ m= $

$ n= $

1

2

$ P(x) $

$ 說明 $

$ P\;(\frac{na+mb}{m+n}) $

1

$ 公式 $

1

G = (8.812982456714685, 0.20227705871836482)
F = (-2.7071620784826615, 0.14635402699410582)
u = Vector((x(Corner[1]), 0), (x(Corner[3]), 0))
v = Vector((0, y(Corner[1])), (0, y(Corner[3])))
O = (0, 0)
Q_2: 0.8 * Corner[1] + 0.2 * Corner[2]
Q_3: (x(Q_2), y(Corner[4]))
poly1, q_1, q_2, q_4, q_3 = Polygon(Corner[1], Q_2, Q_3, Corner[4])
A = DynamicCoordinates(F, floor(x(F)), 0)
B = DynamicCoordinates(G, floor(x(G)), 0)
m_1 = 3 (slider from 1 to 10, step 1)
n_1 = 6 (slider from 1 to 10, step 1)
P: ((n_1 * x(A) + m_1 * x(B)) / (m_1 + n_1), 0)
inputBox1 = Textfield(m_1)
inputBox2 = Textfield(n_1)
a: x(A)
b: x(B)
t_A: "$ A(" + (LaTeX[a]) + ") $"
t_B: "$ B(" + (LaTeX[b]) + ") $"
T_2: "$ ⇒x=" + (LaTeX[a]) + "+" + (LaTeX[FractionText[m_1 / (m_1 + n_1)]]) + " \cdot\;" + (LaTeX[b - a]) + "=" + (LaTeX[FractionText[x(P)]]) + "$"
T_3: "$ ⇒P(\;" + (LaTeX[FractionText[x(P)]]) + "\;) $"
c = LineBisector(A, P)
d = LineBisector(P, B)
C = (-1.812393570894518, -3.4047584874963404)
e = Line(C, xAxis)
D = Intersect(e, c)
E = Intersect(e, d)
f = CircleArc(D, P, A)
g = CircleArc(E, B, P)
t_1: "$ " + (LaTeX[m_1]) + " $"
t_2: "$ " + (LaTeX[n_1]) + " $"
T_1: "$\frac{\overline{PA}}{\overline{AB}}=\frac{x" + (LaTeX[If[a ≥ 0, "-" * abs(a), "+" * abs(a)]]) + "}{" + (LaTeX[b]) + "" + (LaTeX[If[a ≥ 0, "-" * abs(a), "+" * abs(a)]]) + "}=\frac{" + (LaTeX[m_1]) + "}{" + (LaTeX[m_1]) + "+" + (LaTeX[n_1]) + "} $"
h = false
n = 0 (slider from 0 to 3, step 1)
m = 0 (slider from 0 to 3, step 1)
i = false
T_6: "$ ⇒P\;(\;" + (LaTeX[FractionText[(n_1 * a + m_1 * b) / (m_1 + n_1)]]) + "\;) $"
text1: "$已知數線上兩點A(" + (LaTeX[a]) + ")與B(" + (LaTeX[b]) + ")，\;P\;在\overline{AB}上，\;且 \frac{\overline{PA}}{\overline{PB}}=\frac{m}{n} =\frac{" + (LaTeX[m_1]) + "}{" + (LaTeX[n_1]) + "}" + (LaTeX[If[GCD[m_1, n_1] ≠ 1, "=" * FractionText[m_1 / n_1]]]) + "，\;試求P\;點座標.$"
T_5: "$⇒ P\;(\frac{" + (LaTeX[n_1]) + "×" + (LaTeX[If[a < 0, "(-"]]) + "" + (LaTeX[abs(a)]) + "" + (LaTeX[If[a < 0, ")"]]) + "+" + (LaTeX[m_1]) + "×" + (LaTeX[If[b < 0, "(-"]]) + "" + (LaTeX[abs(b)]) + "" + (LaTeX[If[b < 0, ")"]]) + "}{" + (LaTeX[m_1]) + "+" + (LaTeX[n_1]) + "}) $"